In this paper the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations. The outer approximation algorithm is used as a basis to derive a logic-based OA solution method which naturally gives rise to NLP subproblems that avoid zero flows and a disjunctive LP master problem. The NLP subproblems are selected through a set covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer-approximation with Generalized Benders Decomposition it is also shown that it is possible to derive a logic-based method for the latter algorithm. The performance of the proposed algorithms illustrated with two process network problems.